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 A022087 Fibonacci sequence beginning 0, 4. 13
 0, 4, 4, 8, 12, 20, 32, 52, 84, 136, 220, 356, 576, 932, 1508, 2440, 3948, 6388, 10336, 16724, 27060, 43784, 70844, 114628, 185472, 300100, 485572, 785672, 1271244, 2056916, 3328160, 5385076, 8713236, 14098312, 22811548, 36909860, 59721408, 96631268 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n > 1, this sequence gives the number of binary strings of length n that do not contain 0000, 0101, 1010, or 1111 as contiguous substrings (see A230127). - Nathaniel Johnston, Oct 11 2013 REFERENCES A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 18. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (1,1). FORMULA a(n) = 4*F(n) = F(n-2) + F(n) + F(n+2), where F = A000045. a(n) = round( phi^n*(8*phi-4)/5 ) for n>2. - Thomas Baruchel, Sep 08 2004 a(n) = A119457(n+2,n-1) for n>1. - Reinhard Zumkeller, May 20 2006 G.f.: 4*x/(1-x-x^2). - Philippe Deléham, Nov 19 2008 a(n) = F(n+9) - 17*F(n+3), where F=A000045. - Manuel Valdivia, Dec 15 2009 G.f.: Q(0) -1, where Q(k) = 1 + x^2 + (4*k+5)*x - x*(4*k+1 + x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 07 2013 a(n) = Fibonacci(n+3) - Fibonacci(n-3), where Fibonacci(-3..-1) = 2,-1,1. [Bruno Berselli, May 22 2015] MAPLE a:= n-> (Matrix([[4, 0]]). Matrix([[1, 1], [1, 0]])^n)[1, 2]: seq(a(n), n=0..40); # Alois P. Heinz, Aug 17 2008 MATHEMATICA a={}; b=0; c=4; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 9, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 22 2008 *) Table[4 Fibonacci(n), {n, 0, 40}] (* Bruno Berselli, May 22 2015 *) PROG (PARI) a(n)=4*fibonacci(n) \\ Charles R Greathouse IV, Jun 05 2011 (MAGMA) [4*Fibonacci(n): n in [0..40]]; // Vincenzo Librandi, Oct 12 2013 CROSSREFS Cf. A000045. Cf. similar sequences listed in A258160. Sequence in context: A302681 A002368 A299474 * A095294 A190100 A244421 Adjacent sequences:  A022084 A022085 A022086 * A022088 A022089 A022090 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified November 17 12:09 EST 2018. Contains 317276 sequences. (Running on oeis4.)